This is the first book on the subject of spatiotemporal geostatistics. It uses a modern formalism and documents in full the powerful techniques of Bayesian maximum entropy (BME), developed during the past decade to study spatiotemporal phenomena. The book gets to the heart of traditional geostatistics, acknowledges its previous successes, identifies its current limitations, and demonstrates the need for a revised perspective in light of rapidly developing new scientific fields. Modern Spatiotemporal Geostatistics offers a fresh look at the basis of geostatistics, proposing a novel framework that is mathematically rigorous and covers a wide range of physical applications. Such a framework will ensure that geostatistics continuously undergoes two major processes of growth: a unification process with respect to its methods and a discrimination process with respect to its mathematical structure and the way it relates to experience. At the basis of the framework lies the spatiotemporal physical geometry that depends on the local properties of space/time and on the constraints imposed by the natural phenomena. Among the issues treated in depth in Modern Spatiotemporal Geostatistics are important geostatistical operations that depend on physical geometry (including covariance and variogram permissibility, interpolation, and estimation). The epistemic status of space/time mapping is advanced, with its view of the map as a visual representation of a scientific theory regarding the spatiotemporal distribution of the natural variable. Such an approach can be applied in cases in which the space/time variation is non-Gaussian, incorporates the interpolation methods of traditional geostatistics and spatial statistics as special cases, and unifies previously separate classes of random fields including intrinsic, heterogeneous, fractal, and wavelet random fields. Modern Spatiotemporal Geostatistics gives a comprehensive presentation of two distinct elements of BME: the formal part, focused on mathematical structure and logical process, and the interpretive part, concerned with applying the formal part in real-world situations. Major physical-knowledge bases include general knowledge (scientific theories, physical laws, multiple-point statistics, etc.), and specificatory knowledge (hard measurements, various kinds of uncertain or soft data, etc.). The formal part is based on a powerful structure that accounts for many forms of physical knowledge, thus improving the scientific content and accuracy of the space/time map. BME gives nonlinear spatiotemporal estimators, in general, and non-Gaussian laws are automatically incorporated. Multipoint mapping is allowed, and multivariate conditional probability distributions are calculated in a way that guarantees consistency with physical knowledge. BME's formal part is a rigorous generalization that contains kriging techniques as its limiting cases, valid under specific conditions. BME is used with efficiency in a variety of physical problems where kriging techniques are not applicable. Its interpretive part examines the scientific substance of the geostatistical models, and its considerable integration capability allows it to play a vital role in the horizontal integration of disparate scientific disciplines that have resulted from rapid technological development and globalization. BME's interpretive part satisfies certain well-established epistemic ideals (of knowledge acquisition and integration). It has explanatory as well as global prediction features. It allows considerable flexibility in the choice of the appropriate space/time estimate, which is case-specific rather than universal, and, BME assesses estimation uncertainty, processing it along with the space/time analysis and mapping. Modern Spatiotemporal Geostatistics is filled with numerous examples, as well as applications from the Earth sciences, environmental engineering, geography, and human-exposure analysis. The important connections between modern spatiotemporal geostatistics and GIS are discussed, demonstrating the mutual benefits that can accrue from the interaction of geostatisticians and GIS analysts. Modern Spatiotemporal Geostatistics will be useful to geostatisticians, mining and petroleum engineers, geographers, statisticians, civil and environmental engineers, epidemiologists, and health scientists who wish to learn the powerful tools of spatiotemporal analysis and mapping. The book is also suitable as a textbook for graduate and advanced undergraduate students of natural sciences and engineering.